Coordinate Rotation Calculator







Formula

To calculate the new coordinates after rotation:

\[ X = x \cos(\theta) + y \sin(\theta) \]

\[ Y = -x \sin(\theta) + y \cos(\theta) \]

What is Coordinate Rotation?

Coordinate rotation involves rotating a point in the x-y plane by a specified angle about the origin. This is commonly used in various fields such as computer graphics, robotics, and physics to transform coordinates and analyze motion or orientation.

Example Calculation 1

Let's assume the following values:

Step 1: Convert the angle to radians:

\[ \theta = 45 \times \frac{\pi}{180} = 0.7854 \text{ radians} \]

Step 2: Calculate the new X coordinate:

\[ X = 3 \cos(0.7854) + 4 \sin(0.7854) = 4.95 \]

Step 3: Calculate the new Y coordinate:

\[ Y = -3 \sin(0.7854) + 4 \cos(0.7854) = 0.71 \]

Example Calculation 2

Let's assume the following values:

Step 1: Convert the angle to radians:

\[ \theta = 90 \times \frac{\pi}{180} = 1.5708 \text{ radians} \]

Step 2: Calculate the new X coordinate:

\[ X = 5 \cos(1.5708) + 6 \sin(1.5708) = 6 \]

Step 3: Calculate the new Y coordinate:

\[ Y = -5 \sin(1.5708) + 6 \cos(1.5708) = -5 \]